# Methods for Linearly Constrained Problems

• H. A. Eiselt
• Carl-Louis Sandblom
Chapter
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 282)

## Abstract

In this and the following two chapters, several algorithms for solving nonlinear constrained optimization problems will be described. First the most special of all constrained nonlinear programming problems is considered, namely the quadratic programming problem for which the objective function is convex and quadratic and the constraints are linear. In the second section of the chapter methods for the more general problem of optimizing a differentiable convex function subject to linear constraints are discussed. Although every convex quadratic programming problem could be solved also by these more general methods, it is generally preferable to employ quadratic programming methods when possible. As a general principle it is advisable to use more specialized techniques for more specialized problems. Consequently, for a given problem one should select a method (covered in the previous, this, or the next two chapters) from a box as high up in Table 6.1 as possible. The third section considers problems in which the objective function is quadratic, but concave, a difficult case.

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## Authors and Affiliations

• H. A. Eiselt
• 1
• Carl-Louis Sandblom
• 2
1. 1.Faculty of ManagementUniversity of New BrunswickFrederictonCanada
2. 2.Department of Industrial EngineeringDalhousie UniversityHalifaxCanada